Search PubMed⌕ Search

SEARCH · Search PubMed

Results for “Mathematical Concepts”

Search indexed PubMed citations on genomics, clinical trials, systematic reviews and public health. Explore titles, authors and supplied subject terms, then open the PubMed record.

Quote a phrase for an exact phrase match. Source license links do not imply unrestricted reuse.

At least 487 records · Page 27Linked to original sources
PubMed2003

Estimating microbial inactivation parameters from survival curves obtained under varying conditions--the linear case.

When the isothermal semi-logarithmic survival curves of heat inactivated microbial cells or spores are known to be linear it is possible to calculate their survival parameters from curves obtained under nonisothermal conditions, provided that the temperature history ('profile') satisfies certain simple mathematical requirements. These requirements have been identified. The concept was tested by retrieving the survival parameters of a Listeria-like organism from generated survival curves for linear and nonlinear heating profiles on which noise had been superimposed. The availability of such a procedure eliminates the need to determine the survival parameters under perfect isothermal conditions, which are difficult to create for technical reasons. It will also enable determination of the survival parameters in the actual medium of interest, which may contain particles or may be too viscous to be treated in a capillary or narrow tube as is currently done. The method can also be used to assess survival parameters in nonthermal inactivation. A treatment with a dissipating chemical agent or anti-microbial is an example. In principle, the concept can be extended to the more general situation where the isothermal or iso-concentration semi-logarithmic survival curves are clearly nonlinear, but this will require a modification of the model and a different numerical calculation procedure.

Computer Simulation↗
PubMed2003

A semiempirical method for the description of off-center ratios at depth from linear accelerators.

A semiempirical method for the description of the off-center ratios (OCR) at depth from linear accelerators is presented, which is based on a method originally developed for cobalt-60 (60)Co units. The OCR profile is obtained as the sum of 2 components: the first describes an OCR similar to that from a (60)Co unit, which approximates that resulting from the modification of the original x-ray intensity distribution by the flattening filter; the second takes into account the variable effect of the flattening filter on dose profile for different depths and field sizes, by considering the existence of a block and employing the negative field concept. The above method is formulated in a mathematical expression, where the parameters involved are obtained by fitting to the measured OCRs. Using this method, OCRs for various depths and field sizes, from a Philips SL-20 for the 6 MV x-ray beam and a Siemens Primus 23, for both the 6-MV and 23-MV x-ray beams, were reproduced with good accuracy. Furthermore, OCRs for other fields and depths that were not included in the fitting procedure were calculated using linear interpolation to estimate the values of the parameters. The results indicate that this method can be used to calculate OCR profiles for a wide range of depths and field sizes from a measured set of data and may be used for monitor unit calculations for off-axis points using a standard geometry. It may also be useful as a quality control tool to verify the accuracy of lacking profiles calculated by a treatment planning system.

Algorithms↗
PubMed2006

Ordinality and inferential abilities of a grey parrot (Psittacus erithacus).

A grey parrot (Psittacus erithacus), able to label the color of the bigger or smaller object in a pair (I. M. Pepperberg & M. V. Brezinsky, 1991), to vocally quantify < or =6 item sets (including heterogeneous subsets; I. M. Pepperberg, 1994), and separately trained to identify Arabic numerals 1-6 with the same vocal English labels but not to associate Arabic numbers with their relevant physical quantities, was shown pairs of Arabic numbers or an Arabic numeral and a set of objects and was asked for the color of the bigger or smaller one. The parrot's success showed he (a) understood number symbols as abstract representations of real-world collections, (b) inferred the relationship between the Arabic number and the quantity via stimulus equivalence, and (c) understood the ordinal relationship of his numbers.

Animals↗
PubMedDate not supplied

[Urea utilization in growing lambs. 7. NPN- and pure protein-N-utilization at various ages].

The utilization quota of NPN and pure feed protein for body protein synthesis was calculated on the basis of N balance experiments with 15N labelled urea with the help of model concepts of a 3-pool model and its mathematical usage. In lambs weighing 13 kg, the efficiency of amino acid and nucleic acid synthesis in the non-amino acid N pool was 64%. This results in a total utilization quota for NPN and pure protein in the ration of 40% and 60%, resp. Lambs weighing 27 kg showed an efficiency in amino acid and nucleic acid synthesis in the non-AA N pool of 77% and in the AA N pool of 60%. The total utilization quota of NPN was 47% and that of pure protein 56%. The pure protein in the ration was thus about twice as well utilized for total protein synthesis and for protein synthesis for crude protein retention as the NPN compounds in the ration.

Aging↗
PubMed1990

Concepts determining statistical analysis of dental data.

This paper reviews some approaches to statistical analysis of dental data. Often dental data consist of more than one observation per patient which may not be independent, and consequently some standard statistical methods based on independence of all observations are inappropriate. This paper seeks to make the dental researcher and the consulting statistician aware of some of the efficient approaches that can be used to analyse the data successfully. No specialist statistical knowledge is assumed. Rather the goal is to increase awareness of what can be done. The statistical layman is introduced to some basic concepts, while references are given for the mathematically-minded reader. The data of Pack, Coxhead and McDonald is used as a springboard for this discussion.

Data Interpretation, Statistical↗
PubMed2000

Transport and reaction at endothelial plasmalemma: distinguishing intra- from extracellular events.

The pulmonary endothelium is a chemical reactor that modifies blood composition in several ways, including reduction of the oxidized forms of certain redox active substances in the blood. The physiological functions of the transplasma membrane electron transport systems involved in the latter are not fully understood, but an argument is made that they are involved in antioxidant defense. In addition, the experimental approaches used to characterize the process, including studies at whole organ, cell culture, and subcellular levels, along with the use of mathematical modeling, may be representative of the physiome concept wherein a goal is the integration of information obtained at all levels of biological organization. In this article, separation of intra- and extracellular events involved in the disposition of redox active probes within the lungs is the particular example.

Animals↗
PubMed1998

Digital x-ray imaging using amorphous selenium: reduction of aliasing.

Alias reduction is analyzed with the concept of an equivalent presampling filter, and a mathematical approach is established to find the equivalent presampling filter corresponding to specific digital image processing algorithms. The effects of different sampling period T and sampling aperture tau on aliasing artifacts and on the resultant detective quantum efficiency (DQE) for a self-scanned, flat-panel, amorphous selenium detector are obtained. Different effective apertures can be obtained from the same detector by averaging signals over adjacent pixels. It is shown that adding outputs from M adjacent pixels is equivalent to introducing an equivalent presampling filter with special properties. Appropriate selection of the averaging parameters (M and weights) is shown to reduce the aliasing artifact in the resultant image. The effect of incomplete charge collection due to geometrical effects (fill factor) is examined. It is shown that a large fill factor is desirable for aliasing reduction. The relationship between a digital filter applied to the sampled signal and its equivalent presampling analog filter is also established. Analytical formulas for the sampled spectrum of white signal and for the sampled power spectrum of white noise are obtained for aperture functions with a spatially uniform response. These formulas take into accounts aliasing artifacts, signal correlation and aperture function response, and demonstrate the dependence of sampled spectra on T and tau. With these formulas the detective quantum efficiency DQE is derived. It is shown that the resultant DQE depends only on the fill factor and the size of readout electrode tau 0, but is completely independent of the degree or type of pixel averaging. That is, even though the pixel averaging method reduces aliasing it leaves DQE (omega) unchanged. When significant amplifier noise is present the DQE obtained with the pixel averaging method can be better than those obtained with an analog presampling filter. Finally, it is pointed out that the requirement of reducing aliasing artifacts conflicts with other requirements for a detector such as maximizing modulation transfer function (MTF). A careful and practical compromise has to be made by a detector designer in choosing the extent to which the aliasing artifacts are eliminated.

Algorithms↗
PubMed2005

Meeting report: the future and limits of systems biology.

Systems biology has enjoyed explosive growth in both the number of people participating in this area of research and the number of publications on the topic. And yet, the paradigms that underlie the field have not seen a similar expansiveness. Instead, most of these paradigms have been carried over from other fields like engineering, physics, and mathematics. As a result, a small set of concepts dominate the field. The traditional biologist is seen by many as outmoded and tolerated only as a source of data. In this view, the biologist's ideas may even be considered conceptually and theoretically irrelevant. In this Perspective, we take a critical look at some of the paradigms of systems biology and question whether the biologist's ideas, methods, and theories have really become outmoded. We see the future of systems biology as a tight coupling of in vivo and in vitro methods for bioengineering with in silico multicellular modeling and simulation.

Computational Biology↗
PubMed1995

Velocardiofacial syndrome: learning difficulties and intervention.

Velocardiofacial syndrome, delineated in 1978 by Shprintzen, is a multiple genetic disorder, characterised primarily by cleft palate, cardiovascular anomalies, typical facies, and learning disorders. This syndrome with its recurrent pattern of anomalies has significant implications for education as it is linked to a variety of educationally relevant problems including learning difficulties, behaviour disorders, and speech and language deficits. While clinical research advances and new findings in cytogenetics enable early diagnosis and genetic counselling, ramifications of the syndrome in the field of education are still unknown. Learning difficulties should not be viewed solely as a pathological condition and with data on success of intervention, parents and teachers can be apprised of the information. This paper discusses academic characteristics and the effects of intervention with emphasis on interactive computer based instruction on the development of reading, language, spelling, and numeracy skills. Positive effects of computer based instruction on students' self-esteem, motivation, and competence in computer operational skills were also observed and noted. We are encouraged by the enthusiasms of the students for the system, the development of interest in reading, and the transfer of remedial instruction to classroom performance. Comparison of pretest and post-test results indicated significant improvement in reading ability as measured using Neale Analysis. This improvement is in accordance with results obtained using computer testing of specific subskills in reading/language and mathematics.

Abnormalities, Multiple↗
PubMed2007

Causal cognition in human and nonhuman animals: a comparative, critical review.

In this article, we review some of the most provocative experimental results to have emerged from comparative labs in the past few years, starting with research focusing on contingency learning and finishing with experiments exploring nonhuman animals' understanding of causal-logical relations. Although the theoretical explanation for these results is often inchoate, a clear pattern nevertheless emerges. The comparative evidence does not fit comfortably into either the traditional associationist or inferential alternatives that have dominated comparative debate for many decades now. Indeed, the similarities and differences between human and nonhuman causal cognition seem to be much more multifarious than these dichotomous alternatives allow.

Animals↗
PubMed2006

In vivo determination of diffusive transport parameters in a superfused tissue.

To address the hypothesis that functional changes in tissue transport can be related to structural alterations, we combined mathematical modeling with in vivo experimentation. The model concept includes interstitial diffusion and removal by a distributed microvasculature. Transport of solute and water across the peritoneum is measured via a plastic chamber affixed to the abdominal wall of anesthetized Sprague-Dawley rats. Solutions containing [(14)C]mannitol, with or without vasoactive compounds [control (C; n = 10), C + nitroprusside (NP; n = 10), C + norepinephrine (NE; n = 10)], were infused into the chamber, and the volume and tracer concentrations were determined over 60 min to calculate the mass transfer coefficient (MTC) and the water flux. At 60 min, FITC-dextran (500 kDa) was given to mark the perfused vasculature. After euthanasia, the tissue under the chamber was frozen, dried, sliced with a cryomicrotome, and examined with fluorescent microscopy and quantitative autoradiography. The microvessel density (x10(3)/cm(2): NE, 50 +/- 10; C, 180 +/- 7.0; NP, 225 +/- 15) resulted in marked differences (P < 0.05) in water flux (mul.min(-1).cm(-2): NE, 0.1 +/- 0.1; C, 1.6 +/- 0.4; NP, 1.0 +/- 0.2) and in mannitol MTC (x10(3) cm/min: NE, 0.9 +/- 0.3; C, 3.8 +/- 0.3; NP, 3.6 +/- 0.6). Concentration profiles and calculated capillary permeability and tissue diffusivity were significantly different among the groups. These results demonstrate a direct correlation of mass transfer, diffusion, capillary permeability, and water flux with peritoneal vascular density and validate a method by which mechanistic changes in transport may be measured.

Animals↗
PubMed2002

Population genetics and sociobiology: conflicting views of evolution.

This article explores the tension between the population genetics and sociobiological approaches to the study of evolution. Whereas population geneticists, like Stanford's Marc Feldman, insist that the genetic complexities of organisms cannot be overlooked, sociobiologists (many of whom now prefer to call themselves "behavioral ecologists") rely on optimization models that are based on the simplest possible genetics.These optimization approaches have their roots in the classical result known as the fundamental theorem of natural selection, formulated by R. A. Fisher in 1930. From the start there was great uncertainty over the proper interpretation of Fisher's theorem, which became confused with Sewall Wright's immensely influential adaptive landscape concept. In the 1960s, a new generation of mathematical biologists proved that Fisher's theorem did not hold when fitness depended on more than one locus. Similar reasoning was used to attack W. D. Hamilton's inclusive fitness theory. A new theory, known as the theory of long-term evolution, attempts to reconcile the rigorous population genetics approach with the long-standing sociobiological view that natural selection acts to increase the fitness of organisms.

Biological Evolution↗
PubMed2006

Mathematics beliefs and achievement of elementary school students in Japan and the United States: results from the Third International Mathematics and Science Study.

Student self-beliefs are significantly related to several types of academic achievement. In addition, results from international assessments have indicated that students in Japan have typically scored above international averages (D. L. Kelly, I. V. S. Mullis, & M. O. Martin, 2000). In this study, the author examined relationships between mathematics beliefs and achievement of elementary school-aged students in the United States and Japan. The students had participated in the Third International Mathematics and Science Study (TIMSS; A. E. Beaton et al., 1996). The author examined several self-beliefs and used variance estimation techniques for complex sampling designs. The author identified a number of significant relationships between self-beliefs and mathematics achievement. Students who attributed success in mathematics to controllable factors (e.g., hard work, studying at home) showed higher test scores whereas students who attributed success in mathematics at school to external factors (e.g., good luck) tended to earn lower mathematics test scores. These results extend the findings of previous research results because the author examined large national samples of students in cross-cultural settings as part of a comprehensive international assessment.

Attitude↗
PubMed2003

[Difference between numerical and verbal evaluation in the reflection of the attributes].

When evaluating something, both numerical indices (numerical evaluation) and verbal impressions (verbal evaluation) can be used. Previous studies suggest that these evaluations differ in the reflection of typical attributes and atypical attributes of the object being evaluated. In this study, two experiments were performed to examine this suggestion. In both experiments, subjects were required to evaluate the effects of countermeasure programs to prevent plague. In the first experiment, the atypical attributes of the object were manipulated, and in the second experiment, the attributes that participants must pay attention to were manipulated by instruction. In Experiment 1, verbal evaluation reflected more atypical attribute than numerical evaluation, and in Experiment 2, the differences between numerical evaluation and verbal evaluation were systematically changed by the instruction. Some theoretical considerations are presented in the general discussion.

Adult↗
PubMed1999

[1899: the first mathematical description of the pressure-volume diagram by Otto Frank (1865-1944)].

Not until 60 years after 1899 Otto Frank's mathematical formulation of the volume-pressure diagram and his concept of the mechanism of the cardiac work of the left ventricle cardio-physiologists began to rediscover Frank's work systematically. Frank's scientific development proves his constant commitment to and deep interest in understanding and analysing physiological problems mathematically. Consequently Frank worked on the quality and theory of physiological instruments and the problems of measurement, to calculate the influence in experimental research of the cardio-vascular system. Besides Frank's publications on different types of manometers his theory of "Windkessel" function as a model of the mechanics of the left ventricle and the different energies of the cardiac work are of importance even today, although we know only few details of his life as a pupil of Carl Ludwig and Carl von Voit and as a professor of physiology in Giessen and Munich.

Blood Pressure↗